scipy.special.roots_genlaguerre#
- scipy.special.roots_genlaguerre(n, alpha, mu=False)[source]#
Gauss-generalized Laguerre quadrature.
Compute the sample points and weights for Gauss-generalized Laguerre quadrature. The sample points are the roots of the nth degree generalized Laguerre polynomial, \(L^{\alpha}_n(x)\). These sample points and weights correctly integrate polynomials of degree \(2n - 1\) or less over the interval \([0, \infty]\) with weight function \(w(x) = x^{\alpha} e^{-x}\). See 22.3.9 in [AS] for details.
- Parameters:
- nint
quadrature order
- alphafloat
alpha must be > -1
- mubool, optional
If True, return the sum of the weights, optional.
- Returns:
- xndarray
Sample points
- wndarray
Weights
- mufloat
Sum of the weights
References
[AS]Milton Abramowitz and Irene A. Stegun, eds. Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. New York: Dover, 1972.